Find the area of the rectangle if its perimeter is 30cm, and the sum of the lengths of the three sides is 18cm.

Let us denote the lengths of the sides of this rectangle through x and y.

Let x be the length of one side and y the length of the second side of the rectangle.

It is known that the perimeter of this rectangle is 30 cm, therefore, the following relationship holds:

2 * (x + y) = 30.

It is also known that the lengths of the three sides of this rectangle add up to 18 cm.

Since the lengths of two opposite sides of any rectangle are always equal, and of the three sides of a rectangle, two will necessarily be opposite, then the following relation holds:

2x + y = 18.

We solve the resulting system of equations. Subtracting the second equation from the first, we get:

2x + 2y – 2x – y = 30 -18;

y = 12 cm.

Substituting the found value y = 12 into the equation 2x + y = 18, we get:

2x + 12 = 18;

2x = 18 – 12;

2x = 6;

x = 6/2;

x = 3 cm.

Find the area of ​​this rectangle:

12 * 3 = 36 cm ^ 2.

Answer: the area of ​​this rectangle is 36 cm ^ 2.